Question

At what rate percent per annum will the simple interest on a sum of money be $\dfrac{2}{5}$ of the amount in 10 years?
(a) $4\dfrac{1}{2}%$
(b) $5\dfrac{1}{2}%$
(c) $4%$
(d) $5%$

Answer 1

Hint: Assume that the principal amount is ‘x’ and the rate of interest per annum is $y%$. Calculate the simple interest using the formula $SI=\dfrac{P\times R\times T}{100}$. Write the equation based on the data given in the question and simplify the equation to calculate the rate of interest.

Complete step-by-step solution -
We have to calculate the rate of interest per annum at which the simple interest on a sum of money will be $\dfrac{2}{5}$ of the amount in 10 years.
Let’s assume that the principal amount is ‘x’ and the rate of interest per annum is $y%$.
We know the formula for calculating simple interest is $SI=\dfrac{P\times R\times T}{100}$, where SI is the simple interest, P is the amount on which interest is added R is the rate of interest and T is the time for which interest is added.
Substituting $P=x,R=y,T=10$ in the above formula, we have $SI=\dfrac{x\times y\times 10}{100}=\dfrac{xy}{10}$.
We know that the simple interest is $\dfrac{2}{5}$ of the principal amount. Thus, we have $\dfrac{xy}{10}=\dfrac{2x}{5}$.
Simplifying the above equation, we have $\dfrac{y}{10}=\dfrac{2}{5}$.
Cross multiplying the terms of the above equation, we have $5y=2\times 10=20$.
Rearranging the terms of the above equation, we have $y=\dfrac{20}{5}=4%$.
Hence, the rate of interest per annum is $4%$, which is option (c).

Note: We can also solve this question by assuming that the principal is Rs.100 and calculating simple interest on this principal. Write equations based on the data given in the question and solve them to calculate the rate of interest per annum. The value of the rate of interest will be the same as above.